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Peristaltic flow of a heated Jeffrey fluid inside an elliptic duct: streamline analysis

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Abstract

The peristaltic flow of a heated Jeffrey fluid inside a duct with an elliptic cross-section is studied. A thorough heat transfer mechanism is interpreted by analyzing the viscous effects in the energy equation. The governing mathematical equations give dimensionless partial differential equations after simplification. The final simplified form of the mathematical equations is evaluated with respect to the relevant boundary conditions, and the exact solution is attained. The results are further illustrated by graphs, and the distinct aspects of peristaltic flow phenomena are discussed.

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Abbreviations

a 0, b 0 :

ellipse half axes

d :

wave amplitude

λ:

wavelength

\({\bar T_{\rm{w}}}\) :

tube wall temperature

c :

propagation velocity

D h :

hydraulic diameter of ellipse

\({\bar T_{\rm{b}}}\) :

bulk temperature

e :

eccentricity of ellipse

δ :

aspect ratio

ϕ :

occlusion

\(\dot \gamma \) :

rate of shear

Br :

Brickmann number

δ 1 :

relaxation to retardation time ratio

δ 2 :

time retardation parameter

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, 44000, Pakistan

    S. Nadeem & S. Akhtar

  2. Department of Anatomy, School of Dentistry, Shaheed Zulfiqar Ali Bhutto Medical University, Islamabad, 44000, Pakistan

    A. Saleem

Authors
  1. S. Nadeem
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  2. S. Akhtar
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  3. A. Saleem
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Correspondence to S. Nadeem.

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Nadeem, S., Akhtar, S. & Saleem, A. Peristaltic flow of a heated Jeffrey fluid inside an elliptic duct: streamline analysis. Appl. Math. Mech.-Engl. Ed. 42, 583–592 (2021). https://doi.org/10.1007/s10483-021-2714-6

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  • DOI: https://doi.org/10.1007/s10483-021-2714-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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